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The German Aufenthaltstitel is a residence permit for the purpose of the Schengen codes (and probably for every other purpose). As such, it allows you to travel to other Schengen countries. See, for example, Travel documents for non-EU nationals:

If you have a valid residence permit from one of those Schengen countries, it is equivalent to a visa. You may need a national visa to visit non-Schengen countries.

As the last sentence implies, your residence permit does not help you enter the UK or Ireland. France, however, should be no problem.